Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aev2)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=-1/2, a₃>=-1/2

For fixed z and a₁=-3/2, a₂=-1/2, a₃=2

For fixed z and a₁=-3/2, a₂=-1/2, a₃=2, b₁=4

http://functions.wolfram.com/07.27.03.aev2.01

Input Form

HypergeometricPFQ[{-(3/2), -(1/2), 2}, {4, 4}, z] == (64 (8 + 63 z))/(3675 z^3) + (256 (-4049 - 17660 z + 8730 z^2 + 10756 z^3 + 175 z^4) EllipticE[z])/ (1157625 Pi z^3) + (256 (2789 + 6028 z - 15234 z^2 + 2252 z^3 + 4165 z^4) EllipticK[z])/(1157625 Pi z^3)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]